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Kees van Deemter (SSE, Jan '10) Who I am: I... studied logic and philosophy of language –University of Amsterdam (PhD) –Stanford University (postdoc) worked for Philips Electronics on HCI and Language Technology have worked on Natural Language Generation since 1994 –University of Brighton (ITRI) –University of Aberdeen

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Kees van Deemter (SSE, Jan '10) An expression is vague (V) iff it has borderline cases or degrees, e.g. large, small, fast, slow, many, few,... Not just words, e.g., –he came, he saw, he conquered –generic statements Common in all human languages 8 out of top 10 adjectives in BNC Dominant among the first words we learn

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Kees van Deemter (SSE, Jan '10) The pragmatic problem: 2.Why is language vague? Vague expressions seem a bit unclear Is it ever a good idea to be V? Suppose you built an electronic information provider; would you ever want it to offer you V information?

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Kees van Deemter (SSE, Jan '10) The scenario of Lipman (2000, 2006) Airport scenario: I describe Mr X to you, to pick up X from the airport. All I know is Xs height; heights are uniformly distributed across people on [0,1]. If you identify X right away, you get payoff 1; if you dont then you get payoff -1

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Kees van Deemter (SSE, Jan '10) What description would work best? State Xs height precisely If each of us knows Xs exact height then the probability of confusion is close to 0.

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Kees van Deemter (SSE, Jan '10) What description would work best? State Xs height precisely If each of us knows Xs exact height then the probability of confusion is close to 0. If only one property is allowed: Say the tall person if height(X) > 1/2, else say the short person.

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Kees van Deemter (SSE, Jan '10) What description would work best? State Xs height precisely If each of us knows Xs exact height then the probability of confusion is close to 0. If only one property is allowed: Say the tall person if height(X) > 1/2, else say the short person. No boundary cases, so this is not vague! Theorem: under standard game-theory assumptions (Crawford/Sobel), vague communication can never be optimal

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Kees van Deemter (SSE, Jan '10) Natural Language Generation (NLG) is an area of AI with many practical applications (e.g. Reiter and Dale 2000) An NLG program translates input data to linguistic output Essentially the problem of choosing the best linguistic Form for a given Content What does this choice depend on?

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Kees van Deemter (SSE, Jan '10) Our question: When (if ever) is vague communication more useful than crisp communication? The question is not: Can vague communication be of some use? The question is: When is vague communication more useful than crisp communication? –Aside: Is vagueness useful at all?

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Kees van Deemter (SSE, Jan '10) 1. Vicissitudes of measurement [a] Example: One house of 11m height and one house of 12m height 1.the house thats 12m tall needs to be demolished 2.the tall house needs to be demolished Comparison is easier and more reliable than measurement prefer utterance 2 –Measurable as likelihood of incorrect action

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Kees van Deemter (SSE, Jan '10) 1. Vicissitudes of measurement [a] Example: One house of 11m height and one house of 12m height 1.the house thats 12m tall needs to be demolished 2.the tall house needs to be demolished Comparison is easier and more reliable than measurement prefer utterance 2 [But arguably, this utterance is not vague Its vagueness is merely local]

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Kees van Deemter (SSE, Jan '10) Apparent vagueness is frequent the tall house the tallest house Physical exercise is good for young and old regardless of age Bad for bacteria, good for gums gums improve as a result of bacterial death Fast-flowing rivers are deep the faster the deeper (positive correlation between variables)

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Kees van Deemter (SSE, Jan '10) 1. Vicissitudes of measurement [b] Numbers can suggest spurious precision Weather prediction: It will be 23.75 degrees Celcius –Margin of error may be as much as 2 degrees It will be mild does not have this problem [But why not say: approx. 24 degrees ?]

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Kees van Deemter (SSE, Jan '10) E.Peters et al. (2009) When numerical information was accompanied by labels (fair, good, excellent), a greater proportion of variance in evaluation judgments could be explained by the numeric factors –Without labels, the most important information (i.e., factor 1) was not used at all –Without labels, less numerate subjects were influenced by mood (I feel good/bad/happy/upset)

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Kees van Deemter (SSE, Jan '10) [But why should labels be vague?] [Why does English not have a (brief) expression that says Your blood pressure is 150/90 and too high?] Compare You are obese means Your BMI is above 30 and this is dangerous.

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Kees van Deemter (SSE, Jan '10) 4. Future contingencies Indecent Displays Control Act (1981) forbids public display of indecent matter –indecent at the time the law has been parameterised (Waismann 1968, Hart 1994, Lipman 2006) Obama/Volcker: Not too much risk should be concentrated into one bank (Jan. 2010) –opening bid in a policy war

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Kees van Deemter (SSE, Jan '10) 5. Lack of a good metric –Mathematics: How difficult is a proof? (As the reader may easily verify) –Multidimensional measurements: Whats the size of a house? –Esthaetics: How beautiful is a sunset?

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End of survey... on previous answers to the question why language is vague

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Kees van Deemter (SSE, Jan '10) Remainder of this talk Explore tentative new answer: V can oil the wheels of communication Starting point: its almost inconceivable that all speakers arrive at exactly the same concepts

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Kees van Deemter (SSE, Jan '10) The story of the stolen diamond A diamond has been stolen from the Emperor and (…) the thief must have been one of the Emperors 1000 eunuchs. A witness sees a suspicious character sneaking away. He tries to catch him but fails, getting fatally injured (...). The scoundrel escapes. (…) The witness reports The thief is tall, then gives up the ghost. How can the Emperor capitalize on these momentous last words? (book, to appear)

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Kees van Deemter (SSE, Jan '10) This analysis suggests …... that it helps the Emperor to understand tall as having borderline cases or degrees But, borderline cases and degrees are the hallmark of V It appears to follow that V has benefits for search

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Kees van Deemter (SSE, Jan '10) This analysis also suggests …... that degree models offer a better understanding of V than partial models –Compare the first big problem with V Radical interpretation: V concepts dont serve to narrow down search space, but to suggest an ordering of it

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Kees van Deemter (SSE, Jan '10) Objections … Objection 1: Smart search would have been equally possible based on a dichotomous (i.e., classical) model. The idea: You can use a classical model, yet understand that other speakers use other classical models. Start searching individuals who are tall on most models.

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Kees van Deemter (SSE, Jan '10) Objections … Objection 1: Smart search would have been equally possible based on a dichotomous (i.e., classical) model. The idea: you can use a classical model yet understand that other speakers use other classical models. Start searching individuals who are tall on most models Response: Reasoning about different classical models is not a classical logic but a Partial Logic with supervaluations. Presupposes that tall is understood as vague.

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Kees van Deemter (SSE, Jan '10) Objections … Objection 3: Why was the witness not more precise? The idea: Witness should have said the thief was 185cm tall, giving an estimate

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Kees van Deemter (SSE, Jan '10) Objections … Objection 3: Why was the witness not more precise? The idea: Witness should have said the thief was 185cm tall, giving an estimate Response: (1) Why are such estimates vague (approximately 185cm) rather than crisp (185cm =/- 0.5cm)? (2) This can be answered along the lines proposed.

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Kees van Deemter (SSE, Jan '10) Objections … Objection 4: This contradicts Lipmans theorem The idea: Lipman (2006) proved that every V predicate can be replaced by a crisp one that has a utility at least as high.

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Kees van Deemter (SSE, Jan '10) Summing up Why information reduction is useful is well understood Why this should involve borderline cases is less clear. (Lipmans question) Several tentative answers have been published. (Survey) A new answer, based on mismatches in perception and benefits for search –complements earlier answers

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Kees van Deemter (SSE, Jan '10) Not Exactly: in Praise of Vagueness. Oxford University Press, Jan. 2010 Part 1: Vagueness in science and daily life. Part 2: Linguistic and logical models of vagueness. Part 3: Working models of V in Artificial Intelligence.